MODELING THE SIZE DEPENDENT STATIC AND DYNAMIC PULL-IN INSTABILITY OF CANTILEVER NANOACTUATOR BASED ON STRAIN GRADIENT THEORY

Abstract

It is well-established that mechanical behavior of nanoscale systems is size dependent. In this paper, strain gradient elasticity theory is used for mathematical modeling of size dependent electromechanical instability of cantilever nanoactuator. The nanoactuator is modeled using Euler–Bernoulli beam theory and equation of motion is derived using Hamilton's principle. In order to solve the nonlinear governing equation, reduced order method (ROM) is employed. The dynamic pull-in instability of the nanoactuator is investigated through plotting the time history and phase portrait of the system. Static and dynamic pull-in voltage of nanoactuator as a function of dimensionless length scale parameters is determined. The obtained results show that when thickness of the nanoactuator is comparable with the intrinsic material length scales, size effect can substantially influence the pull-in behavior of the system.